QAIPM-2002-Ph-2844: NEET 2002 Physics - Class 11 AIPM-2002-Ph-2844 Solution: When an oscillator completes 100 oscillations its amplitude…

This is a case of damped vibration as the amplitude of vibration is decreasing with time. Amplitude of vibrations at any instant t is given by a = a 0 e � b t , where a 0 is the initial amplitude of vibrations and b is the damping constant. Now, when t = 100T, a = a 0 / 3   [T is time period] Let the amplitude be a _ at t = 200T. i.e. after completing 200 oscillations. _ a = a 0 / 3 = a 0 e � 100 T b    ...(i) and a _ = a 0 e � 200 T b ...(ii) From (i), 1 3 = e _ 100 T b _ e _ 200 T b = 1 / 9 From (ii), a _ = a 0 _ 1 9 = a 0 9 _ The amplitude will be reduced to 1/9 of initial value.